Active cage model of glassy dynamics

We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture somec haracteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a cross-over between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage, and the ratio of the hopping length to the cage size.